As you can see, this question is hard enough even with the formulas provided.
This is no mere matter of plugging values into a formula and cranking out the
answer. This question is more algebraic than that and takes a little thought.
It’s really a word problem. It describes in words a mathematical situation (in
this case, geometric) that can be translated into algebra. The pivot in this
situation is that the cone and sphere have equal volumes. You’re looking for
the height h in terms of x, and fortunately you can express both volumes in
terms of those two variables. Be careful. Both formulas include r, but they’re
not the same r’s. In the case of the cone, r = 2x, but in the case of the sphere, r
= 3x:
Now write an equation that says that the expressions for the two volumes are
equal to each other, and solve for h:
(A) x(B)(C)
(D) 20 x(E) 27 x